Two efficient algorithms are proposed to seek the sparse representation on high-dimensional Hilbert space. By proving that all the calculations in Orthogonal Match Pursuit (OMP) are essentially inner-product combinations, we modify the OMP algorithm to apply the kernel-trick. The proposed Kernel OMP (KOMP) is much faster than the existing methods, and illustrates higher accuracy in some scenarios. Furthermore, inspired by the success of group-sparsity, we enforce a rigid group-sparsity constraint on KOMP which leads to a noniterative variation. The constrained cousin of KOMP, dubbed as Single-Step KOMP (S-KOMP), merely takes one step to achieve the sparse coefficients. A remarkable improvement (up to 2,750 times) in efficiency is reported for S-KOMP, with only a negligible loss of accuracy.